Those apparently bizarre words might actually end up being uttered next year because of a quirk in Obamacare that could financially penalize a number of workers and their families.

That quirk means that for some people, it will be more economical to have an employer not offer health insurance subsidies for them and their families—and for the entire family to then instead be able to buy insurance with government subsidies on the Obamacare state health exchanges.

"For a lot of people, that may be a better deal," said Jonathan Wu, co-founder of the price-comparison site ValuePenguin.com. "We're talking like thousands of dollars."

Wu noted that companies might be able to shed health-care costs as a result of the quirk, too.

"Our analysis suggests that employees and employers across the country should sit down and discuss the potential merits of discontinuing employer-sponsored plans," ValuePenguin.com said in a new report. "The company would end up saving money while the employee would benefit from thousands of dollars in tax subsidies—a clear win-win for both parties."

What Wu calls one of several "weird" unintended effects of the Affordable Care Act—effects that lead to some less-than-affordable outcomes—stems from a rule that was adopted by the Health and Human Services Department last winter and goes into effect in 2014.

Under the ACA, popularly known as Obamacare, a worker whose employer offers company-subsidized health insurance that costs the worker less than or equal to 9.5 percent of household income is considered to be receiving "affordable coverage."

Workers with access to that supposedly affordable coverage from their employers are not eligible to reject it and instead buy insurance on the Obamacare state exchanges using government subsidies in the form of tax credits. Those credits are available to households whose incomes fall below 400 percent of federal poverty levels, which for a family of four is $94,200.

But HHS has ruled that the affordability test will consider only the cost to workers of buying insurance from their company's plan for themselves—not that of insuring their entire family.

In other words, even if the cost of obtaining coverage for a worker's entire family exceeds 9.5 percent of household income, that family cannot potentially save money by buying subsidized insurance on the state health exchanges.

"Where it really hurts is where the company subsidizes only the employee and not the rest of the family," he added.

The potential financial hit to families is becoming more apparent with the approach of Oct. 1—the date when all federal and state-run Obamacare exchanges are scheduled to begin enrolling people in plans—and as exchanges release data about the premiums their plans charge.

Wu demonstrated the phenomenon with data from New York state's health insurance exchange and the hypothetical example of a family of four earning $50,000 per year. He assumed they were being offered, in the employer plan, insurance costing $13,646 annually for the entire family, and $4,788 annually for coverage for just the employee.

In his scenario, the company paid 50 percent of the employee's premium for coverage, but nothing for the premiums for the rest of the family.

In that scenario, the employee's premium cost would be $2,394 per year—well under the 9.5 percent affordability test level. Thus, the entire family would be disqualified from using federal subsidies to buy insurance on the Obamacare exchanges.

The family then would have two options.

Option one would be for the entire family to get insured under the employer plan at a net cost of $11,252—an amount that takes into account the company's subsidy to the employee.

Option two would be for the employee to buy insurance from his company's plan, at an out-of-pocket cost of $2,394. The three other members of his family would then buy insurance on the New York exchange at a cost of of $7,120—for a total of $9,514.

But Wu pointed out that if the company didn't pay any part of the employee's premium for the company-offered insurance, the entire family would significantly benefit financially under the Obamacare rule.

In that situation, a worker would be on the hook for all of the $4,788 annual premium cost for the company plan. That's more than the 9.5 percent income affordability test—and his family would thus be eligible for government subsidies on the New York state health exchange.

By using those subsidies, the entire family's total cost after purchasing the second cheapest "Silver" plan on that exchange would be just $3,365 a year.

That's nearly $6,000 less than the cheapest scenario available to the same family if the worker was offered employer-subsidized insurance, Wu noted.

"The employee could simply ask the employer to keep the $2,400 [subsidy] so that the insurance would not qualify as affordable," the ValuePenguin report said.

ValuePenguin also pointed out that even if the employer paid half of the premiums for the family in the company-offered plan, the total cost to the family would be $6,823 annually. That's nearly $3,500 more than a plan that would be available to them on the New York exchange if they hadn't received the company's subsidies in the first place.

In that situation, Wu said, "You would rather say, 'Don't give me that coverage.' "